Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

7. Non-Right Triangles

Law of Sines

Trigonometry

7. Non-Right Triangles

Law of Sines

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2:33 minutes

Problem 1

Textbook Question

In oblique triangle ABC, A = 34°, B = 68°, and a = 4.8. Find b to the nearest tenth.

Verified step by step guidance

Step 1: Use the Law of Sines, which states $ \frac{a}{\sin A} = \frac{b}{\sin B} $.

Step 2: Substitute the known values into the equation: $ \frac{4.8}{\sin 34^\circ} = \frac{b}{\sin 68^\circ} $.

Step 3: Solve for $ b $ by multiplying both sides by $ \sin 68^\circ $: $ b = \frac{4.8 \cdot \sin 68^\circ}{\sin 34^\circ} $.

Step 4: Calculate the sine values using a calculator: $ \sin 34^\circ $ and $ \sin 68^\circ $.

Step 5: Substitute the sine values back into the equation to find $ b $ to the nearest tenth.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Law of Sines

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. This can be expressed as a/sin(A) = b/sin(B) = c/sin(C). This law is particularly useful for solving oblique triangles, where not all angles and sides are known, allowing us to find unknown side lengths or angles.

Oblique Triangle

An oblique triangle is a triangle that does not contain a right angle. It can be either acute (all angles less than 90°) or obtuse (one angle greater than 90°). Solving oblique triangles often requires the use of the Law of Sines or the Law of Cosines, depending on the information given and what needs to be found.

Angle Measures

In trigonometry, angles are typically measured in degrees or radians. In this problem, angles A and B are given in degrees, which is a common unit for measuring angles in triangles. Understanding how to work with angle measures is crucial for applying trigonometric laws effectively, especially when calculating unknown angles or sides.